The two triangles are similar.

What is the value of x?



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x =

The number of students who passed with I, II, and III divisions are 35, 70, and 49, respectively.

We have,

Let's denote the number of students who passed with I, II, and III divisions as x, y, and z, respectively.

Given that the total number of students who appeared in the examination is 210, and 56 students failed, we can calculate the number of students who passed:

Number of students who passed = Total students - Number of students who failed

= 210 - 56

= 154

According to the given ratio, the number of students who passed with I, II, and III divisions are in the ratio of 5:10:7.

We can express this ratio in terms of x, y, and z as:

x : y : z = 5 : 10 : 7

To find the actual number of students who passed with I, II, and III divisions, we can set up the following equation based on the ratio:

5k + 10k + 7k = 154

22k = 154

k = 154 / 22

k = 7

Now, we can find the number of students who passed with I, II, and III divisions:

Number of students who passed with I division = 5k = 5 x 7 = 35

Number of students who passed with II division = 10k = 10 x 7 = 70

Number of students who passed with III division = 7k = 7 x 7 = 49

Therefore,

The number of students who passed with I, II, and III divisions are 35, 70, and 49, respectively.

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Answer:

[tex]\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300[/tex]

Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.

Step-by-step explanation:

you already have a cosine. You might as well change that sine in a cosine too:

[tex]8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0[/tex]

(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace [tex]x=cos\theta[/tex] and let's solve

[tex]8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8[/tex]

At this point we're back to the replacement. We have two options

[tex]cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°[/tex]

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{5.4} \end{cases} \\\\\\ x=\sqrt{ 4^2 + 5.4^2}\implies x=\sqrt{ 16 + 29.16 } \implies x=\sqrt{ 45.16 }\implies x\approx 6.7[/tex]

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

–6x – 3

Step-by-step explanation:

To find the expression that is equivalent to 3(–2x – 1), we need to distribute the 3 to each term inside the parentheses.

When we distribute 3 to –2x, we get:

3 * –2x = –6x

When we distribute 3 to –1, we get:

3 * –1 = –3

Therefore, the expression equivalent to 3(–2x – 1) is:

–6x – 3.

Answer:

-6x - 3

Step-by-step explanation:

Distribute 3 through the parenthesis:

[tex]\sf{3(-2x-1)}[/tex]

[tex]\sf{3*(-2x)+3*(-1)}[/tex]

[tex]\sf{-6x-3}[/tex]

Hence, the expression that is equivalent  to 3(-2x - 1) is -6x - 3.

Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

The minimum is the smallest value in the data set:

Minimum: 4

The maximum is the largest value in the data set:

Maximum: 21

The median is the middle value in the data set. Since there are an even number of values in this data set, we take the average of the two middle values:

Median: (10 + 12)/2 = 11

To find the quartiles, we first need to find the median of the lower half and upper half of the data set:

Lower half: 4, 7, 9, 10

Upper half: 12, 15, 20, 21

Median of lower half: (7 + 9)/2 = 8

Median of upper half: (15 + 20)/2 = 17.5

The first quartile (Q1) is the median of the lower half of the data set:

1st Quartile: 8

The third quartile (Q3) is the median of the upper half of the data set:

3rd Quartile: 17.5

Therefore: Minimum: 4 Maximum: 21 Median: 11 1st Quartile: 8 3rd Quartile: 17.5

I hope this helps! Let me know if you have any other questions.

Answer:

  B.  2

Step-by-step explanation:

You want the predicted number of missed shots after 8 weeks if the trend line equation is ...

  y = -1/2x +6

Using x=8 in the given equation, we find the prediction to be ...

  y = -1/2(8) +6 = -4 +6 = 2

The number of missed shots is predicted to be 2.

__

Additional comment

We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.

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The classification of the given polynomial is cubic polynomial, the correct option is C.

We are given that;

The equation=3x^3-x^2-x+4

Now,

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

Degree of 3x^3=3

Degree of x^2=2

Degree of x=1

The heighest degree of the polynomial is three of 3x^3.

Therefore, by the polynomial the answer will be cubic polynomial.

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answer:

a) 8

_ or 50%

16

b) 8 or 50%

_

16

c) 11 or 68.75%

_

16

Step-by-step explanation:

To find the area of the square all you need to do is to find the length of the hypotenuse of the triangles

this will help us find the length of the square if we are given the values of the shorter lengths as shown up

we can calculate the length of the hypotenuse by using the Pythagorean theorem

[tex] \sqrt{a^{2} + b^{2} } = c[/tex]

we are given the sides of the shorter lengths being 5 and 3 we can then substitute them into the formula

let us label the missing length the hypotenuse as x

[tex] \sqrt{ {3}^{2} + {5}^{2} } = x[/tex]

[tex] \sqrt{34} = x[/tex]

[tex]5.83[/tex]

we get that 5.83 rounded to two decimal places is the length of the hypotenuse

we also know that it is the length of the square so

5.83 × 5.83 = Area of Square

34cm² = Area of Square

Answer:

$120

Step-by-step explanation:

Job1:

       To find the tax, multiply the payment per week ($70) by 0.1.

         Tax = payment * tax rate

                = 70 * 10%

                [tex]\sf = 70 * \dfrac{10}{100}\\\\ = \$7[/tex]

Now, to find his earning after deduction of tax, subtract 7 from 70.

Amount after deduction of tax = 70 - 7

                                                  = $ 63

Job2:

       Tax = 60 * 5%

              = 60 * 0.05

               = $3

  Amount after deduction = 60 - 3

                                           = $ 57

Total amount Byron takes home = 63 + 57

                                                      = $120

Answer:

x = -6 and y =5

Step-by-step explanation:

2x + 5y = 13    (call this equation '1')

-4x - 3y = 9    (call this '2')

multiply '1' by 2

4x + 10y = 26       (call this '3')

eliminate by adding '2' and '3':

(-4 + 4)x + (-3 + 10)y = 9 + 26

7y = 35

y = 5

sub that into '1':

2x + 5(5) = 13

2x + 25 = 13

2x = 13 - 25 = -12

x = -6

sub both x = -6 and y =5 into '2' to make sure everything adds up:

-4(-6) - 3(5) = 24 - 15 = 9

so x = -6 and y = 5

Answer:

Step-by-step explanation:

There are several reasons why a student would choose to study in a province different from their home province. Some of the reasons include:

To gain a new perspective and experience different cultures.

To take unique classes that are not available in their home province.

To learn history through immersive experiences.

To improve their ability to adapt.

To gain independence.

To gain international experience and a global network.

To immerse themselves in another language.

The quantities in the two columns cannot be compared due to the absence of specific point values. D.

The given question presents two columns, Column A and Column B, representing the slopes of lines through different sets of points.

The actual points themselves are not provided in the question.

Without the specific point values, it is not possible to determine the slope values or compare the quantities in Column A and Column B.

The slope of a line is determined by the change in the y-coordinate divided by the change in the x-coordinate between two points.

Since the coordinates of the points are missing, it is impossible to calculate the slopes accurately or make any comparison between the quantities in Column A and Column B.

Without the points, it is not possible to determine the slopes or establish any relationship between the quantities in Column A and Column B.

To draw any conclusions or comparisons, the coordinates of the points through which the lines pass are crucial.

Without that information, we lack the necessary data to assess the slopes and make any meaningful comparison.

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Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Answer:

Step-by-step explanation:

To determine whether y is a function of x in the equation x+4y=8, we can solve for y in terms of x:

x + 4y = 8

4y = 8 - x

y = (8 - x)/4

Copy

Since every value of x corresponds to exactly one value of y, y is a function of x.

Answer:

x = 8 and y = -4

Step-by-step explanation:

3x + 4y = 8    (call this equation '1')

x - y = 12      (call this '2')

multiply '2' by 3:

3x - 3y = 36  (call this '3')

subtract '1' from '3':

(3x - 3y = 36)  -  (3x + 4y = 8)

0x + -7y = 28

-7y = 28

y = -4.

sub that back into '1':

3x + 4y = 8

3x + 4(-4) = 8

3x - 16 = 8

3x = 8 + 16 = 24

x = 8.

sub both y =-4 and x =8 into '2' to check if everything adds up:

x - y = 12

8 - -4 = 8 + 4 = 12

so x = 8 and y = -4

Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

The volume of the container is 180 cubic meters.

Given,

Length of the container = 4 meters

Width of the container = 3 meters

Height of the container = 15 meters

Let the container is a cuboid, as the shape of the container isn't mentioned.

Now, we know that,

The volume of a cuboid = Length of the cuboid × Width of the cuboid × Height of the cuboid

Therefore, the volume of the given container of cuboid shape = 4 × 3 × 15 cubic meters.

                                                             = 180 cubic meters.

Hence, the volume of the container is 180 cubic meters.

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There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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(a) The expected value of playing the game is 0.

(b) Heather can expect to break even in the long run.

To find the expected value of playing the game, we need to calculate the weighted average of the possible outcomes.

Expected value calculation:

The probability of selecting each ball is the same since Heather replaces the ball in the bag each time.

The probability of selecting any particular number is 1/8.

Expected value = (Probability of outcome 1 × Value of outcome 1) + (Probability of outcome 2 × Value of outcome 2) + ... + (Probability of outcome 8 × Value of outcome 8)

Expected value = (1/8 × 1) + (1/8 × 2) + (1/8 × 5) + (1/8 × 6) + (1/8 × 8) + (1/8 × 10) + (1/8 × (-13)) + (1/8 × (-13))

Expected value = (1/8) + (2/8) + (5/8) + (6/8) + (8/8) + (10/8) + (-13/8) + (-13/8)

Expected value = 26/8 - 26/8

Expected value = 0

Since the expected value of playing the game is 0 On average, she neither gains nor loses money over multiple plays of the game.

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The nth roots of perfect nth powers evaluates to:

[tex]\sqrt[5]{-32}[/tex] = -2

[tex]-\sqrt[4]{256}[/tex] = -4

Perfect nth Power is an integer which is obtained from multiplying a single integer by itself n times.

The nth root of a Perfect nth Power is an integer which when multiplied by itself n times it will produce the original value under the radical.

To find the nth roots of perfect nth powers with signs, you can use the following steps:

1. Write the perfect nth power as a product of nth roots.

2. Find the nth root of each factor.

3. Combine the nth roots to get the final answer.

[tex]\sqrt[5]{-32}[/tex] = [tex]\sqrt[5]{-2^{5} }[/tex]

         = -2

-[tex]\sqrt[4]{256}[/tex] = -[tex]\sqrt[4]{4^{4} }[/tex]

           = -4

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The end behavior of the graph of the function f(x) = -5(4x - 2) as x approaches infinity can be described as follows:

As x approaches infinity (or positive infinity), the value of 4x becomes infinitely large compared to the constant -2. Therefore, we can ignore the constant (-2) and simplify the function as f(x) = -5(4x) = -20x.

Since the coefficient of x is negative (-20), the graph of the function will decrease without bound as x approaches infinity. In other words, the function will approach negative infinity (or -∞) as x becomes infinitely large.

Similarly, as x approaches negative infinity, the value of 4x becomes infinitely large in the negative direction. Thus, we can simplify the function as f(x) = -5(4x) = -20x.

Since the coefficient of x is negative (-20), the graph of the function will also decrease without bound as x approaches negative infinity. Therefore, the function will approach negative infinity (or -∞) as x becomes infinitely negative.

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The values of x we found are x = 14 and x = 0.

To find the value of x in the given set of equations and expressions, we need to solve each equation individually and substitute the value of x into subsequent expressions. Let's solve each equation step by step:

Equation 21: 21 = B + 2 + 3x

To isolate 3x, we subtract 2 from both sides: 21 - 2 = B + 3x

19 = B + 3x

Equation 25: 25 = 2x - 3

To isolate 2x, we add 3 to both sides: 25 + 3 = 2x

28 = 2x

Divide both sides by 2: x = 14

Equation 24: 24 = G + LL + F

We don't have enough information to solve this equation since we don't know the values of G, LL, and F.

Equation 22: 22 = 5x + H + 10

To isolate 5x, we subtract H and 10 from both sides: 22 - H - 10 = 5x

12 - H = 5x

Equation 23: 23 = x + 8 + x + 3 + 12

Combining like terms: 23 = 2x + 23

Subtracting 23 from both sides: 0 = 2x

Divide both sides by 2: x = 0

Therefore, the values of x we found are x = 14 and x = 0.

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The measure of arc XYL + measure of arc VUL + measure of arc VIX = 360°.  Therefore, the correct answer is option D.

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference.

From the given circle, measure of arc XYL + measure of arc VUL + measure of arc VIX = 360° (Complete angle)

Therefore, the correct answer is option D.

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Answer:

the number of meters in the milky way

Step-by-step explanation:

becuse the world is infinite

Answer:

Let's assume the number of adults attending the performance is represented by 'x', and the number of children attending is represented by 'y'.

According to the given information, the entrance fee for adults is R50 each, and for children is R20 each.

The total amount raised by the school is R31,400. We can write an equation based on the total amount raised:

50x + 20y = 31,400

This equation represents the total value of the entrance fees paid by adults and children.

To solve this equation, we need another equation to relate the variables 'x' and 'y'.

Since we don't have any other information about the number of adults or children, we cannot determine their relationship based on the given information. Therefore, we cannot find a unique solution for 'x' and 'y' unless there is additional information provided.

If there is additional information or if you have any specific values for 'x' or 'y', I can assist you in solving the equation and finding the number of adults and children attending the performance.

Step-by-step explanation: